1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with special relativity problem (off by a factor of 2)

  1. Jul 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Special Relativity A.P French Problem 1-9

    An eccentric billionaire decides to sterilize his 106 liter swimming pool by boiling the water in it. For heating purposes he uses the fusion reaction:

    1H + 3H → 4He + radiant energy

    Assuming the heating system is 20% efficient, how much does he pay for the tritium (3H) to raise the pool temperature from 20°C to 100°C? It takes 4.2 joules to raise 1g of water through 1°C. Tritium costs about $5 per cm3 of gas at STP.

    2. Relevant equations

    E = mc2

    3. The attempt at a solution

    Total energy required:
    [tex] E_{total} = 4.2 \frac{J}{g°C} * 10^9 g * 80°C = 3.36*10^{11} J[/tex]

    Energy Generated per reaction:
    [tex] E_{reaction} = m_{diff} * c^{2}[/tex]
    [tex] E_{reaction} = ((1.0081 + 3.0170) - 4.0039)amu * 1.6603*10^{-27} * (3*10^{8}\frac{m}{s})^{2} = 3.1682 * 10^{-12} J [/tex]

    Atoms per cubic centimeter of gas at STP:

    [tex]\frac{atoms}{cm^3}=6.0221*10^{23} * \frac{1}{22.711} * 10^{-3} = 2.6516 * 10^{19}[/tex]

    Final Result (1/0.2) is to account for 20% efficiency:
    [tex]cost=$5*\frac{1}{0.2} * \frac{E_{total}}{\frac{E_{reaction}}{\frac{atoms}{cm^3}}} =~ $100,000[/tex]

    The answer in the book is $50,000, which would imply I'm off by a factor of two. I've looked over this for some time and can't see my mistake. Can anyone help me spot what I've missed?
     
    Last edited: Jul 21, 2013
  2. jcsd
  3. Jul 21, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    It is "molecules per cubic centimeter", not atoms.

    Tritium gas is T2.



    That is a weird setup. He will spend the first billion (at least) for the fusion reactor.
     
  4. Jul 21, 2013 #3
    I think irrationality is a requirement in physics textbooks problems.

    Thanks for the help, that would certainly yield the right answer. Is this just something that should have been obvious from a chemistry standpoint? My chemistry is really rusty.
     
  5. Jul 22, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Hmm... it is something you should know, but there is a big difference between knowing it and thinking of it.
     
  6. Jul 22, 2013 #5
    Chemistry or physics, the thing to remember is that gases are made of molecules, and the Avogadro constant is how many molecules a mole of gas contains. Then you just need to find what a molecule of the given gas is.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help with special relativity problem (off by a factor of 2)
Loading...